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Permutation Entropy: A Natural Complexity Measure for Time Series

Christoph Bandt and Bernd Pompe
Phys. Rev. Lett. 88, 174102 – Published 11 April 2002
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Abstract

We introduce complexity parameters for time series based on comparison of neighboring values. The definition directly applies to arbitrary real-world data. For some well-known chaotic dynamical systems it is shown that our complexity behaves similar to Lyapunov exponents, and is particularly useful in the presence of dynamical or observational noise. The advantages of our method are its simplicity, extremely fast calculation, robustness, and invariance with respect to nonlinear monotonous transformations.

  • Received 19 June 2001

DOI:https://doi.org/10.1103/PhysRevLett.88.174102

©2002 American Physical Society

Authors & Affiliations

Christoph Bandt and Bernd Pompe

  • Institute of Mathematics and Institute of Physics, University of Greifswald, Greifswald, Germany

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Vol. 88, Iss. 17 — 29 April 2002

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